'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (98.3%) in the period of the last 5 years, the total return of 280.7% of ProShares UltraPro QQQ is higher, thus better.
- Looking at total return, or performance in of -18.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (27.2%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Which means for our asset as example:- Compared with the benchmark SPY (14.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 30.7% of ProShares UltraPro QQQ is higher, thus better.
- Compared with SPY (8.4%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of -6.5% is lower, thus worse.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of ProShares UltraPro QQQ is 75.2%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at volatility in of 70.8% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.7%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 53.6% of ProShares UltraPro QQQ is larger, thus worse.
- Looking at downside volatility in of 50.3% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.4%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Applying this definition to our asset in some examples:- Looking at the risk / return profile (Sharpe) of 0.37 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.58)
- During the last 3 years, the Sharpe Ratio is -0.13, which is lower, thus worse than the value of 0.33 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Which means for our asset as example:- The downside risk / excess return profile over 5 years of ProShares UltraPro QQQ is 0.53, which is lower, thus worse compared to the benchmark SPY (0.82) in the same period.
- Looking at excess return divided by the downside deviation in of -0.18 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.47).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Ratio of 43 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Downside risk index in of 53 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (10 ).

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -81.7 days of ProShares UltraPro QQQ is lower, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum reduction from previous high of -81.7 days is smaller, thus worse.

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- The maximum days below previous high over 5 years of ProShares UltraPro QQQ is 702 days, which is greater, thus worse compared to the benchmark SPY (488 days) in the same period.
- Looking at maximum days below previous high in of 702 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (488 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 225 days of ProShares UltraPro QQQ is larger, thus worse.
- Compared with SPY (177 days) in the period of the last 3 years, the average time in days below previous high water mark of 333 days is greater, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical and do not account for slippage, fees or taxes.